A Level Mathematics Paper 4 · Mechanics practice papers
50 marks · 1h 15m. Each generated paper follows the 9709 Paper 4 · Mechanics format, with the same number and style of questions as the real exam, and comes with a Cambridge-style mark scheme.
Three particles A, B and C, of masses 2 kg, 3 kg and 2 kg, lie in that order in a straight line on a smooth horizontal surface. A is projected towards B with speed 5 m s−1; B and C are at rest. After A collides with B, A moves with speed 1 m s−1 in the opposite direction.
(a)
Find the speed of B immediately after the collision.
[2]
(b)
B then collides with C and the two particles coalesce. Find their common speed.
[2]
(c)
Find the total loss of kinetic energy in the two collisions, and state whether there is any further collision. Give a reason.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
4 m s−1
2 × 5 = 2 × (−1) + 3v M1 4 A1
2
(b)
2.4 m s−1
momentum conserved for B and C M1 2.4 A1
2
(c)
9.6 J; no further collision because A moves away from the combined particle
KE before = ½ × 2 × 52M1 KE after for all particles M1 9.6 J A1 no further collision: A moves in the opposite direction B1
4
Question 2Structured · 10 marksA* challenge
Particle A of mass 3 kg lies on a rough horizontal table. It is attached to a light inextensible string that passes over a smooth pulley at the edge of the table. Particle B of mass 3 kg hangs from the other end, 1 m above the floor. The coefficient of friction between A and the table is 0.25. The system is released from rest with the string taut. A does not reach the pulley.
(a)
Find the acceleration of the system and the tension in the string.
[5]
(b)
Find the speed of B when it hits the floor.
[2]
(c)
B does not rebound. Find the total distance moved by A before it comes to rest.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
3.75 m s−2, 18.8 N
friction = 0.25 × 30 = 7.5 B1 Newton’s second law for A M1 Newton’s second law for B M1 a = 3.75 A1 T = 18.8 A1
5
(b)
2.74 m s−1
v2 = 2as M1 2.74 A1
2
(c)
2.5 m
deceleration of A = 2.5 m s−2B1 extra distance = 1.5 m M1 total 2.5 A1
3
Question 3Structured · 4 marks
A child of mass 51 kg slides from rest down a slide of length 32 m. The bottom of the slide is 19 m below the top. The child reaches the bottom with speed 10 m s−1. Find the work done against resistance and the average resistance force.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
7140 J; 223 N
PE loss = mgh B1 work–energy M1 7140 A1 223 A1
4
Question 4Structured · 6 marks
A particle moves in a straight line. Its velocity t seconds after leaving O is v = 3t(6 − t) m s−1 for 0 ≤ t ≤ 6.
(a)
Find the maximum velocity.
[3]
(b)
Find the distance travelled in the 6 seconds.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
27 m s−1
dvdt = 0 M1 t = 3 A1 27 A1
3
(b)
108 m
integrate M1 limits 0 to 6 M1 108 A1
3
Question 5Structured · 4 marks
A car accelerates uniformly from 10 m s−1 to 19 m s−1 in 6 s. Find (a) the acceleration, (b) the distance travelled in this time.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a) 1.5 m s−2 (b) 87 m
v = u + at M1 1.5 A1 s = ½(u + v)t M1 87 A1
4
Question 6Structured · 4 marks
A car of mass 1400 kg travels on a straight horizontal road against a resistance of 900 N. The engine works at 45 kW. Find the acceleration when the speed is 20 m s−1.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
0.964 m s−2
Driving force = P ÷ v M1 2250 N A1 F − R = ma M1 0.964 A1
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in